(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Give an example of an infinite collection of nested open sets.

[itex] o_1 \supseteq o_2 \supseteq o_3 \supseteq o_4 ..... [/itex]

Whose intersection [itex] \bigcap_{n=1}^{ \infty} O_n [/itex] is

closed and non empty.

2. Relevant equations

A set [itex] O \subseteq \mathbb{R} [/itex] is open if for all points, [itex] a \in O [/itex]

there exists an [itex] \epsilon [/itex] neighborhood [itex] V_{\epsilon}(a) \subseteq O [/itex]

3. The attempt at a solution

It seems like if we started with the open interval (0,1) and then took a smaller interval that was nested inside the original interval, and then just kept doing this until we enclosed one point in the interval.

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# Homework Help: Nested open sets?

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